Also the Riemann sphere can be extended to a wheel by adjoining an element . The Riemann sphere is an extension of the complex plane by an element , where for any complex . However, is still undefined on the Riemann sphere, but defined in wheels.

Wheels discard the usual notion of division being a binary operator, replacing it with multiplication by a unary operator similar (but not identical) to the reciprocal, such that becomes shorthand for , and modifies the rules of algebra such that

The subset is always a commutative ring if negation can be defined as above, and every commutative ring is such a subset of a wheel. If is an invertible element of the commutative ring, then . Thus, whenever makes sense, it is equal to , but the latter is always defined, even when .